This proposal is directed toward improving tomographic imaging in diagnostic radiology and nuclear medicine. It is predicted on the claim that significant advances will be achieved in the fidelity of the images that are reconstructed from the raw detector measurements of the tomographic scanner, and in the fidelity of the displays of volumes and surfaces that are derived from these images, by changing the type of basic elements (called "basis functions"), with which the image is built in the computer, from the conventional voxel type to a type recently developed by the Principal Investigator. These new basic elements are localized in space (as are the voxel basis functions) but they also have a number of very desirable properties not shared by voxel basis functions (they are rotationally symmetric, their Fourier transforms are effectively localized, they have continuous derivatives of any desired order and which can be calculated from convenient formulas, and their x-ray transforms have similar desirable properties). Due to these properties, they are ideal for forming faithful digital image representations of the biological structures that have influenced the raw tomographic scanner data. The specific aims are to develop mathematical theory, efficient computer algorithms, application-specific implementations and evaluation criteria for (1) methods of iterative reconstruction from projections, and (2) methods of display of volumes and surfaces, using the recently-developed basis functions. The research plans for these aims represent a focused 3- year program based on computer simulations and on PET data of realistic phantoms. For specified imaging tasks, we will evaluate the significance level at which the hypothesis that algorithms perform a task equally well can be rejected in favor of the alternative hypothesis that the performance of one is superior to that of another. The basis functions of the image representation are at the essential core of all methods for iterative reconstruction and of all methods for 3D display, irrespective of the imaging modality (e.g., CT, PET, SPECT, MRI). The development of new basis functions and image representations will enable the full potential of scanners for functional imaging in emission tomography (PET and SPECT) to be realized by means of computer algorithms that incorporate realistic models of the data acquisition process.